Measures of Dispersion Test

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Measures of Dispersion Test - 38

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Weekly Quiz Competition

Question 1
1 / -0

Given $$\sum (x-\bar{x})^2=48, \bar{x}=20$$ and $$n=12$$. The coefficient of variation is.

A
$$25$$

B
$$20$$

C
$$30$$

D
$$10$$

Solution
Question 2
1 / -0

The sum of the squares of deviations of 10 items about mean 50 is 250 .The coefficient of variation is

A
10%

B
50%

C
30%

D
none of these

Solution

$$\textbf{Step -1: Find the standard deviation.}$$
$$\text{It is given, }$$
$$\text{Mean, }\overline{x}=50,$$
$$n=10\text{ and }$$
$$\sum(x-\overline{x})^2=250$$
$$\therefore\text{Standard deviation}=\sqrt{\dfrac{\sum(x-\overline{x})^2}{n}}$$
$$=\sqrt{\dfrac{250}{10}}$$
$$=5$$
$$\textbf{Step -2: Find the coefficient of variance.}$$
$$\text{Coefficient of variation}=\dfrac{\text{Standard deviation}}{\text{Mean}}\times100\%.$$
$$=\dfrac{5}{50}\times100\%$$
$$=10\%$$
$$\textbf{Hence, option A is correct.}$$
Question 3
1 / -0

The probability distribution of a random variable $$X$$ is given below:
$$X=x$$ 0 1 2 3
$$P(X=x)$$ $$\frac{1}{10}$$ $$\frac{2}{10}$$ $$\frac{3}{10}$$ $$\frac{4}{10}$$
Then the variance of $$X$$ is

A
1

B
2

C
3

D
4

Solution

$$E[x^2]=0+1^2\cdot \displaystyle \frac{2}{10}+2^2\cdot \frac{3}{10}+3^2\cdot \frac{4}{10}=\frac{[2+12+36]}{10}=5.0$$
$$E[x]=0+\displaystyle \frac{2}{10}+2\cdot \frac{3}{10}+3\cdot \frac{4}{10}=\frac{[2+6+12]}{10}=2$$
$$\therefore$$ Var (x) $$= E[x^2] - E[x]^2 = 5-2^2=1$$
Question 4
1 / -0

Which of the following are limitations of range?

A
It is not based on all the values.

B
As long as the minimum and maximum values remain unaltered, any change in other values does not affect range.

C
It can not be calculated for open-ended frequency distribution.

D
All of these
Question 5
1 / -0

Which one of the following is not a measure of dispersion?

A
Quartile

B
Range

C
Mean Deviation

D
Standard Deviation
Question 6
1 / -0

The formula of students t-distribution is_____________.

A
$$ t = \dfrac {s}{\sqrt{n}}$$

B
$$ t = \dfrac {| \bar{X} - \mu |}{s}$$

C
$$ t = \dfrac {{\dfrac{| \bar{X} - \mu |}{s}}}{\sqrt{n}}$$

D
$$ t = \dfrac {{\dfrac {\sqrt{n}}{| \bar{X} - \mu |}}}{s}$$

Solution

The correct formula for calculating students t-distribution is given in option C, where s is the standard deviation of the sample and n is the sample size. The t distribution is used to estimate population parameters when the sample size is small.
Question 7
1 / -0

While constructing Lorenz Curve we take into account _________.

A
cumulative percentages of the variable on Y axis and cumulative percentages of frequencies on X-axis

B
cumulative percentages of the variable on X axis and cumulative percentages of frequencies on Y-axis

C
cumulative variable on X axis and cumulative frequencies on Y-axis

D
None of these
Question 8
1 / -0

Which of the following is true?

A
Standard Deviation is not affected by the value of the constant from which deviations are calculated.

B
The value of the constant does not figure in the standard deviation formula

C
Standard Deviation is Independent of Origin.

D
All of these
Question 9
1 / -0

Coefficient of Quartile Deviation =

A
[ Q(3) + Q(1) ] / [ Q(3) - Q(1) ]

B
Q(3) - Q(1)

C
[ Q(3) - Q(1) ] / [ Q(3) + Q(1) ]

D
[ Q(3) - Q(1) ] / 2
Question 10
1 / -0

Lorenz curve is based on which of the following?

A
Cumulative frequencies as a percentage

B
Cumulative totals of class mid points as a percentage

C
Both A and B

D
None of these

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$$X=x$$	0	1	2	3
$$P(X=x)$$	$$\frac{1}{10}$$	$$\frac{2}{10}$$	$$\frac{3}{10}$$	$$\frac{4}{10}$$

Measures of Dispersion Test - 38

Result

Measures of Dispersion Test - 38

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Question 1

$$25$$

$$20$$

$$30$$

$$10$$

Solution

Question 2

10%

50%

30%

none of these

Solution

Question 3

1

2

3

4

Solution

Question 4

It is not based on all the values.

As long as the minimum and maximum values remain unaltered, any change in other values does not affect range.

It can not be calculated for open-ended frequency distribution.

All of these

Question 5

Quartile

Range

Mean Deviation

Standard Deviation

Question 6

$$ t = \dfrac {s}{\sqrt{n}}$$

$$ t = \dfrac {| \bar{X} - \mu |}{s}$$

$$ t = \dfrac {{\dfrac{| \bar{X} - \mu |}{s}}}{\sqrt{n}}$$

$$ t = \dfrac {{\dfrac {\sqrt{n}}{| \bar{X} - \mu |}}}{s}$$

Solution

Question 7

cumulative percentages of the variable on Y axis and cumulative percentages of frequencies on X-axis

cumulative percentages of the variable on X axis and cumulative percentages of frequencies on Y-axis

cumulative variable on X axis and cumulative frequencies on Y-axis

None of these

Question 8

Standard Deviation is not affected by the value of the constant from which deviations are calculated.

The value of the constant does not figure in the standard deviation formula

Standard Deviation is Independent of Origin.

All of these

Question 9

[ Q(3) + Q(1) ] / [ Q(3) - Q(1) ]

Q(3) - Q(1)

[ Q(3) - Q(1) ] / [ Q(3) + Q(1) ]

[ Q(3) - Q(1) ] / 2

Question 10

Cumulative frequencies as a percentage

Cumulative totals of class mid points as a percentage

Both A and B

None of these

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